The present invention relates to a control arithmetic apparatus for performing, for example, PID (Proportional, integrational and Differential) control or IMC (Internal Model Control) to calculate a manipulated variable on the basis of the error (deviation) between a set point and a controlled variable or the like and, more particularly, to a control arithmetic apparatus having the function of suppressing an overshoot accompanying the application of an disturbance and a control arithmetic method.
Conventionally, an apparatus using PID control is generally used as a versatile control arithmetic apparatus that can be used for an indefinite controlled system. As shown in FIG. 5, a conventional PID control arithmetic apparatus 10 is comprised of a host computer 11 for outputting an error Er by subtracting a controlled variable PV from an input set point SP and a control arithmetic section 12 for calculating a manipulated variable MV from the error Er output from the subtracting section 11 and outputting it to a controlled system 13.
Letting CPID be the transfer function of the control arithmetic section 12 and P be the transfer function of the controlled system 13, the manipulated variable MV is obtained from the transfer function CPID of the control arithmetic section 12 according to equation (1):
MV=CPID(SPxe2x88x92PV)xe2x80x83xe2x80x83(1)
The transfer function CPID can be expressed as
CPID=Kg{1+(1/Tis)}(1+Tds)/(1+xcex7Tds)xe2x80x83xe2x80x83(2)
where Kg is a proportional gain, Ti is the integration time, Td is the differentiation time, and xcex7 is the constant (e.g., xcex7=0.2).
In this case, in controlling temperature and pressure, the transfer function P of the controlled system 13 can be approximated by equation (3):
P =Kp exp(xe2x88x92Lps)/(1+Tps)xe2x80x83xe2x80x83(3)
where Kp is the gain, Tp is the time constant, and Lp is the dead time. The gain Kp provides static characteristics for the controlled system 13; the time constant Tp, time delay characteristics (dynamic characteristics); and the dead time Lp, dead time characteristics (dynamic characteristics).
According to the known adjustment formula in a control theory or the known IMC theory proposed by M. Morari, in order to satisfy both stability and quick response of control, PID parameters (proportional gain Kg, integration time Ti, and differentiation time Td) are preferably given as follows:
Kg =xcex1Tp/(KpLp)xe2x80x83xe2x80x83(4)
Ti=xcex2Tpxe2x80x83xe2x80x83(5)
Td=xcex3Lpxe2x80x83xe2x80x83(6)
where xcex1, xcex2, and xcex3 are constants (e.g., xcex1=0.6, xcex2=1, and xcex3=0.5). If PID parameters are set for the control arithmetic section 12, excellent control characteristics can be normally obtained.
According to the above conventional PID control arithmetic apparatus, in a steady state of temperature control, when a disturbance occurs, e.g., a temporary drop in temperature occurs, the manipulated variable MV is updated to restore the temperature. At the time of occurrence of a disturbance like a temporary drop in temperature, the temperature is automatically restored without updating the manipulated variable MV after a lapse of a relatively long period of time. In such a case, updating the controlled variable PV by using the PID control unit apparatus amounts to excessive manipulated variable correction. Consequently, as a phenomenon reflecting in the controlled variable PV, an excessive control response represented by an overshoot occurs, as shown in FIG. 6A.
As an example of a temporary drop in temperature as a disturbance, a phenomenon occurs, in which the temperature in a reaction furnace temporarily drops when a boat on which a plurality of semiconductor wafers are mounted is inserted into the reaction furnace in a batch type CVD (Chemical Vapor Deposition) furnace used for the manufacture of semiconductors. In the batch type CVD furnace shown in FIG. 7, reference numeral 61 denotes a boat, 62, a reaction furnace, 63-1 to 63-5, heaters for heating zones 1 to 5 in the reaction furnace 62; 64-1 to 64-5, sensors for measuring the temperatures (controlled variables PV) in the zones 1 to 5, and 65-1 to 65-5, PID control arithmetic apparatuses. The PID control arithmetic apparatuses 65-1 to 65-5 calculate the manipulated variables MV and output them to the heaters 63-1 to 63-5 to set the temperatures in the zones 1 to 5 to the temperature designated by the set point SP.
For temperature control in a semiconductor manufacturing process of forming a thin film by using a chemical reaction, an overshoot is a serious undesired phenomenon. Under the circumstances, a control arithmetic apparatus is disclosed in Japanese Patent Laid-Open No. 4-039701 (reference 1). This apparatus has the function of suppressing an overshoot by temporarily correcting the set point SP supplied to a PID control arithmetic section to a value near the controlled variable PV when a situation in which the controlled variable PV approaches the set point SP is detected, as shown in FIG. 8A.
The control arithmetic apparatus disclosed in reference 1 corrects the set point SP upon detection of a situation in which the controlled variable PV approaches the set point SP. For this purpose, the overshoot suppressing function is activated in the second half of last period in a series of controlled variable changes in the time interval between the instant at which the controlled variable PV deviates from the set point SP upon application of a disturbance and the instant at which the controlled variable PV is settled at a value near the set point. For this reason, at the time of occurrence of a disturbance for which the controlled variable PV changes at a high speed, like a temporary drop in temperature at the time of loading of a boat into the batch type CVD furnace, the overshoot suppressing function does not work for an excessive manipulated variable correction immediately after the application of a disturbance, which should be suppressed.
Consequently, as shown in FIGS. 8A and 9A, only a control result that does not differ much from that obtained by a general control arithmetic apparatus having no overshoot suppressing function can be obtained. That is, even if the overshoot suppressing function is activated upon detection of a situation in which the controlled variable PV approaches the set point SP, it is substantially too late to perform effective control. As described above, in the conventional control arithmetic apparatus, if a disturbance for which the controlled variable PV changes at high speed is applied, an overshoot cannot be suppressed.
It is an object of the present invention to provide a control arithmetic apparatus and method which can suppress an overshoot even if a disturbance for which the controlled variable changes at high speed is applied.
In order to achieve the above object, according to the present invention, there is provided a control arithmetic apparatus comprising first calculation means for calculating an error of a controlled variable on the basis of a controlled variable and set point for a controlled system, detection means for detecting, in control cycles, on the basis of the error output from the first calculation means whether a disturbance is applied, second calculation means for calculating an error correction amount on the basis of a magnitude of the error output from the first calculation means when application of a disturbance is detected, convergence operation means for performing convergence operation such that the error correction amount output from the error correction amount calculation means gradually converges to 0, and control arithmetic means for calculating a manipulated variable on the basis of the error output from the first calculation means and an error correction amount after the convergence operation which is output from the convergence operation means.